Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates

Applications of Mathematics

Volumn 48, Issue 1, 2003, Pages 49-66

  Slodička, Marián ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

nonlocal boundary condition; parabolic IBVP; parameter identification

Indexed keywords

EID: 84867989624     PISSN: 08627940     EISSN: 15729109     Source Type: Journal    
DOI: 10.1023/A:1022954920827     Document Type: Article

References (17)

1. D. Andreucci R. Gianni 1996 Global existence and blow up in a parabolic problem with nonlocal dynamical boundary conditions Adv. Differential Equations 1 729 752
2. D. N. Arnold F. Brezzi 1985 Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates RAIRO Modél. Math. Anal. Numér. 19 7 32
3. J. H. Bramble P. Lee 1994 On variational formulations for the Stokes equations with nonstandard boundary conditions RAIRO Modél. Math. Anal. Numér. 28 903 919
4. H. De Schepper M. Slodička 2000 Recovery of the boundary data for a linear second order elliptic problem with a nonlocal boundary condition ANZIAM Journal (C) 42 518 535
5. A. Friedman: Partial Differential Equations. Robert E. Krieger Publishing Company, Hungtinton, New York, 1976.
6. A. Friedman: Variational Principles and Free-Boundary Problems. Wiley, New York, 1982.
7. J. Kačur: Method of Rothe in Evolution Equations. Teubner Texte zur Mathematik Vol. 80. Teubner, Leipzig, 1985.
8. J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967.
9. C.V. Pao: Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York, 1992.
10. J. Heywood R. Rannacher S. Turek 1996 Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations Internat. J. Numer. Methods Fluids 22 325 352
11. K. Rektorys: The Method of Discretization in Time and Partial Differential Equations. Reidel Publishing Company, Dordrecht-Boston-London, 1982.
12. M. Slodička: A monotone linear approximation of a nonlinear elliptic problem with a non-standard boundary condition. In: Algoritmy 2000 (A. Handlovičová, M. Komorníková, K. Mikula and D. Ševčovič, eds.). Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry, Bratislava, 2000, pp. 47-57.
13. M. Slodička 2001 Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition RAIRO Modél. Math. Anal. Numér. 35 691 711 (Pubitemid 33570244)
14. M. Slodička H. De Schepper 2002 On an inverse problem of pressure recovery arising from soil venting facilities Appl. Math. Comput. 129 469 480 (Pubitemid 34524979)
15. R. Van Keer L. Dupré J. Melkebeek 1999 Computational methods for the evaluation of the electromagnetic losses in electrical machinery Arch. Comput. Methods Engrg. 5 385 443
16. R. Van Keer, M. Slodička: Numerical modelling for the recovery of an unknown flux in semilinear parabolic problems with nonstandard boundary conditions. In: Proceedings European Congress on Computational Methods in Applied Sciences and Engineering, Barcelona (E. Onate, G. Bugeda and B. Suárez, eds.). Barcelona, 2000.
17. R. Van Keer, M. Slodička: Numerical techniques for the recovery of an unknown Dirichlet data function in semilinear parabolic problems with nonstandard boundary conditions. In: Numerical Analysis and Its Applications (L. Vulkov, J. Wasniewski and P. Yalamov, eds.). Springer, 2001, pp. 467-474. (Pubitemid 33242276)